What does p = mv (momentum) really mean?

[A.T.]

Shall I remind that it was a certain A.T. who asserted the following:

It's only significance is its conservation under certain conditions. That's the only reason why it is defined this way.

Yep, and that claim can only be proven wrong, by pointing out another significance of momentum. Let me know when you have found one.

 

[voko]

Yep, and that claim can only be proven wrong, by pointing out another significance of momentum. Let me know when you have found one.

I hope you realize that I could do so trivially by defining the term "significance" any way I see fit, exploiting yet another fallacy in your reasoning?

 

[A.T.]

...defining the term "significance" any way I see fit...

Yes, you can play some semantic games with yourself, if that pleases you. Have fun.

 

[Dale]

Voko, as a third party, I also think that your question is very convoluted. I wouldn't answer it either.

I don't think that I would go so far as to say that momentum is only significant due to its conservation, but I cannot think of a counter example. For example, in a pendulum problem the momentum of the pendulum is not conserved, and momentum is not used to solve pendulum problems.

 

[Dale]

I cannot think of a counter example.

I just thought of a counter-example. Momentum is used to find wavelength per deBroglie. That is a significance of momentum which could be important regardless of conservation.

 

[vjacheslav]

Would you to give any conditions of conserving momentum, please?

 

[voko]

Yes, you can play some semantic games with yourself, if that pleases you. Have fun.

The semantic player here is you. You made a categorical statement involving an undefined notion. Your statement is not falsifiable as such. When confronted with critique, your required your critics to prove your statement wrong via a counter-example, which is impossible because it is not falsifiable. Your statement is fallacious, and your attitude, now that your fallacies have been demonstrated, is questionable.

Voko, as a third party, I also think that your question is very convoluted.

I think I made them - at the very least I was genuinely trying - to make them simple yes/no questions. The reason is that the original statement felt wrong to me, but at that point I had not really formulated to myself why it felt wrong, so I tried to use those questions to understand what was really meant and why that felt wrong to me. But we have moved on since then. The true reason is, the statement is meaningless. "Significance" is subjective. It means something to some person, and something different to another. It is entirely possible that A.T.'s perception of his statement is fully tautological: momentum's significance is in its conservation, period; that requires no proof and cannot be proven wrong; but that is quite possibly not true to anyone else.

 

[A.T.]

I just thought of a counter-example. Momentum is used to find wavelength per deBroglie. That is a significance of momentum which could be important regardless of conservation.

Yes, that would be a counter-example, unless the derivation of the deBroglie equations depends on momentun conservation itself. I wasn't thinking about quantum mechanics in the context of this sub-forum.

 

[olivermsun]

It is entirely possible that A.T.'s perception of his statement is fully tautological: momentum's significance is in its conservation, period; that requires no proof and cannot be proven wrong; but that is quite possibly not true to anyone else.

Well, in the Newtonian viewpoint, momentum is the quantity which is conserved in inertial frames; you could call this somewhat tautological, since inertial frames are the ones in which momentum is conserved.

Nevertheless, it's a pretty profound concept that, having been given a name, "the thing which is conserved" follows the Second Law.

 

[DrStupid]

Nevertheless, it's a pretty profound concept that, having been given a name, "the thing which is conserved" follows the Second Law.

In non-inertial frames of references momentum is not conserved but still follows the Second Law. Fictitious forces just violate the Third Law.

 

[olivermsun]

So what you're saying is, if you posit additional, fictitious forces you can even make a non-inertial frame conserve momentum?

 

[DrStupid]

So what you're saying is, if you posit additional, fictitious forces you can even make a non-inertial frame conserve momentum?

No. If the frame of reference conserves momentum it would be no longer non-inertial.

 

[olivermsun]

You say the second law is still obeyed in a non-inertial (e.g., rotating) frame, but this is only because the (apparently spontaneous) change in momentum is explained by introducing a fictitious force.

Without the fictitious force, which doesn't obey the third law (and therefore does not obey conservation of momentum), motion in the rotating frame actually does not obey the 1st and 2nd laws.

Also, it's called fictitious because it doesn't conserve "facts."

So now I'm getting confused: what is actually being conserved, and what is not here?

 

[DrStupid]

You say the second law is still obeyed in a non-inertial (e.g., rotating) frame, but this is only because the (apparently spontaneous) change in momentum is explained by introducing a fictitious force.

Fictitious forces result from the second law in non-inertial frames - not vice versa. Nothing needs to be explained or introduced here.

So now I'm getting confused: what is actually being conserved, and what is not here?

As fictitious forces violate the third law (that's why they are called fictitious) they do not conserve momentum.

 

[olivermsun]

Fictitious forces result from the second law in non-inertial frames - not vice versa. Nothing needs to be explained or introduced here.

Now you're turning circular. Forces (fictitious or otherwise) don't "result" from the second law in any frame AFAIK. What would be "vice versa"—the second law resulting from fictitious forces in non-inertial frames?

As fictitious forces violate the third law (that's why they are called fictitious) they do not conserve momentum.

I always thought they are called fictitious (or pseudo-) because they don't arise from any interaction of bodies, but only from the "interaction" of reference frames.

But anyway this is getting silly. You must have missed all the smileys I put in my previous posts.

Let's let them carry on with the original inane discussion.

 

[Dale]

Also, it's called fictitious because it doesn't conserve "facts."

Facts (i.e. the outcome of specific experimental measurements) are not conserved to begin with. However, they are invariant, including in non-inertial frames.

There is a big difference between "conserved" (does not change over time) and "invariant" (is agreed on by different reference frames). Mass is invariant and conserved. Energy is conserved but not invariant. Proper acceleration is invariant but not conserved. Position is neither conserved nor invariant.

 

[olivermsun]

Facts (i.e. the outcome of specific experimental measurements) are not conserved to begin with. However, they are invariant, including in non-inertial frames.

Just to clarify something: I meant "facts" as in "the fact that a force exists." In the example we're talking about, no force exists—only a pseudo force that allows Newton's second law to be apparently obeyed in the non-inertial frame.

There is a big difference between "conserved" (does not change over time) and "invariant" (is agreed on by different reference frames).

The body which is at rest or in motion in the non-inertial frame experiences a change in momentum (changes over time) which is apparently not caused by any force. (Of course we know that it's actually the frame of reference, not the body, that is in nonuniform motion.)

 

[DrStupid]

Forces (fictitious or otherwise) don't "result" from the second law in any frame AFAIK.

The second law says F=dp/dt - without any restrictions.

What would be "vice versa"—the second law resulting from fictitious forces in non-inertial frames?

Vice versa means the second law is valid in non-inertial frames because there are fictitious forces. Actually there are fictitious forces in non-inertial frames because the second law is valid.

I always thought they are called fictitious (or pseudo-) because they don't arise from any interaction of bodies, but only from the "interaction" of reference frames.

Thats the violation of the third law. The first and second law say there is a force. The third law says that's not a force.

 

[olivermsun]

The second law says F=dp/dt - without any restrictions.

The usual interpretation is that the 2nd law is asserted to hold in an inertial frame (i.e., under the conditions in which the 1st law holds).

Vice versa means the second law is valid in non-inertial frames because there are fictitious forces. Actually there are fictitious forces in non-inertial frames because the second law is valid.

We introduce fictitious forces because we want to proceed as if the second law were valid even in the non-inertial frame.

On the other hand, it's pretty clear if you consider, e.g., the motions of equation in a rotating frame of reference, that the pseudo-forces look nothing like what we think of as forces in an inertial frame.

Thats the violation of the third law. The first and second law say there is a force. The third law says that's not a force.

You could try and read it that way I suppose…

 

[DrStupid]

The usual interpretation is that the 2nd law is asserted to hold in an inertial frame (i.e., under the conditions in which the 1st law holds).

The usual interpretation is that all three laws are asserted to hold in an inertial frame. If at least one of them is violated the system is not inertial. As the third law is designed to conserve momentum it would stand to reason that that this law is violated in non-inertial frame. Assuming the second law to be invalid is not useful.

We introduce fictitious forces because we want to proceed as if the second law were valid even in the non-inertial frame.

We get the fictitious forces if we assume the second law to be valid. Nothing has to be introduced here.

 

[olivermsun]

The usual interpretation is that all three laws are asserted to hold in an inertial frame.

I can agree with that. The 2nd law is indeed one of the three laws.

We get the fictitious forces if we assume the second law to be valid. Nothing has to be introduced here.

This is true. If you start with an incorrect but convenient assumption, then nothing else has to be introduced.

 

[DrStupid]

If you start with an incorrect but convenient assumption, then nothing else has to be introduced.

Try to proof that the assumption is not correct.

 

[olivermsun]

I think I'll pass. We already have equations of motion in rotating frames which have been "proofed" to be consistent with Newton's 2nd law, provided the 2nd law is assumed to hold in inertial frames.

 

[porcupine137]

Questions such as "What really is momentum?" or "What really is mass?" etc. are utterly useless as far as the science is concerned. Answering them adds nothing to the predictive or explanatory power of the theories they derive from. All you have to know is that momentum is well-defined both mathematically and operationally. Anything else that might be said about them is simply philosophical sophistry.

I'll have to disagree. I bet neither S.R. nor G.R. would have been discovered with that sort of mindset, just for starters.

 

[porcupine137]

Talk to someone with no idea of the Maths involved in Physics and you usually hear a pretty poor model of the World. Maths is so crucial to understanding at any but the very superficial level. Imagine trying to have a conversation about Finances without a common knowledge of the Arithmetic of Interest and Profit. The consequence of not using appropriate Maths is constantly being demonstrated by how people are regularly conned into bad deals. The numbers (and the Algebra) always count.
I think many of the preceding comments have been made by people who do, in fact, have an appreciation of the Maths but it is so familiar to them that they are hardly aware of it.

Yes, but don't forget also that getting buried in pure math or looking at nothing but the math seems to be what those who have never made any of the great discoveries in physics do.

 

[Dale]

I'll have to disagree. I bet neither S.R. nor G.R. would have been discovered with that sort of mindset, just for starters.

Hmm, I don't see the connection. Relativity was not developed to answer "what really is momentum?" As far as I know, anyway.

Yes, but don't forget also that getting buried in pure math or looking at nothing but the math seems to be what those who have never made any of the great discoveries in physics do.

I don't think that anyone is advocating that. A balance is clearly needed, but ignoring or avoiding the math is not balanced and is crippling to understanding of physics. In most threads here lack of math is much more of a problem than excessive math.

 

[sophiecentaur]

I'll have to disagree. I bet neither S.R. nor G.R. would have been discovered with that sort of mindset, just for starters.

SR, GR and all the rest were arrived at by trying to apply 'rules' to observed data. 'Real' Science does not look for 'what things really are'. Science has had its fingers burned too many times to risk statements about 'reality'. If you choose to interpret the present state of knowledge as reality then there's not much of interest left for you in Science. I think it is exactly that "mindset" that allows people to make progress and not the assumption that we are at the end of the road.

 

[sophiecentaur]

Yes, but don't forget also that getting buried in pure math or looking at nothing but the math seems to be what those who have never made any of the great discoveries in physics do.

So you expect to find an ultimate description that doesn't involve any Maths and rigour?
PS I was just listening to BBC Radio 4, to a Science Programme and someone made the comment that most researchers never manage to come up with anything 'really important'. There are just not enough breakthroughs to go round. Most of what your average Joe can expect to contribute is a minor tiffle here or there to produce a very small nudge in the right direction - by scrupulous application of the rules and with great experimental care. 99% perspiration and 1% inspiration, as they say.

 

[porcupine137]

So you expect to find an ultimate description that doesn't involve any Maths and rigour?

Where did I ever remotely say such a thing??

 

[sophiecentaur]

Where did I ever remotely say such a thing??

You seemed, to me, to imply some sort of mutual exclusivity between the two. I would very much doubt that Albert E. arrived at his ideas in the absence of a lot of data and without the Maths being constantly at his side. I know he used to talk in terms of stories and dreams he had but I'd bet that was largely post hoc rationalising, for the sake of an audience and his books.

 

[porcupine137]

Hmm, I don't see the connection. Relativity was not developed to answer "what really is momentum?" As far as I know, anyway.

First, I never said everything has to be based upon the sole question "what is momentum".

Anyway, there was a lot of imagination going on when he came up with S.R. and G.R.

equivalence principle (which actually does, in a way, start getting back to momentum), etc. many have come up with the Unruh effect but just imaging and visualizing various implications. etc. etc.

Thinking about mass can get one to Higgs mechanism, etc.

We are also probably talking a bit at cross purposes. I'm being very loose and you are being very strict.

 

[porcupine137]

You seemed, to me, to imply some sort of mutual exclusivity between the two. I would very much doubt that Albert E. arrived at his ideas in the absence of a lot of data and without the Maths being constantly at his side. I know he used to talk in terms of stories and dreams he had but I'd bet that was largely post hoc rationalising, for the sake of an audience and his books.

Well I definitely never remotely meant to imply a mutual exclusivity between the two, so my mistake if it came across the wrong way. I absolutely, completely do not mean to imply that. I don't remotely agree with that statement at all.

And I'd guarantee that stuff was not all post hoc rationalizing. That's the sort of the stuff that all too many lack and sure they can calculate up a storm and handle every equation with a breeze, but do they come up with the major new ideas very often?

 

[sophiecentaur]

I can see we're not real disagreeing much on this one (as if . . . .!). But, having talked with some very (gobsmackingly) clever people in other fields of study (coding and modulation in communications), I have usually noticed that they tend to arrive at their conclusions as a result of loads of Maths but then the presentation to others has required the use of more metaphor. Fact is that the Maths is such a powerful language for Science that it is bound to play a massive part in any frontier bashing.

 

[russ_watters]

That's the sort of the stuff that all too many lack and sure they can calculate up a storm and handle every equation with a breeze, but do they come up with the major new ideas very often?

Who are "they"? I've never once heard a criticism of a physicist from other physicists that they were too mathematical. On the contrary, the math is the most critical part of developing a new theory.

So the direct answer I would give to your question is: Yes, always.

 

[Dale]

First, I never said everything has to be based upon the sole question "what is momentum".

Anyway, there was a lot of imagination going on when he came up with S.R. and G.R.

Sure, but I don't think that any of it was of the form " what really is ...". In fact, if anything I think his approach was more about taking things at face value rather than trying to uncover some hidden reality. The imagination came in figuring out how seemingly incompatible propositions could be compatible.

I doubt that any of the participants of this thread are opposed to imagination, but just by experience have never seen a valuable outcome from "what really is" questions. I think most of the opposition is simply to the specific form of question.